#!/usr/bin/python

"""Project Euler Solution 018

Copyright (c) 2011 by Robert Vella - robert.r.h.vella@gmail.com

Permission is hereby granted, free of charge, to any person obtaining a copy
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copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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THE SOFTWARE.
"""

import cProfile

def get_answer():
    """Question:
    
    By starting at the top of the triangle below and moving to adjacent numbers
    on the row below, the maximum total from top to bottom is 23.
    
    3
    7 4
    2 4 6
    8 5 9 3
    
    That is, 3 + 7 + 4 + 9 = 23.
    
    Find the maximum total from top to bottom of the triangle below:
    
    75
    95 64
    17 47 82
    18 35 87 10
    20 04 82 47 65
    19 01 23 75 03 34
    88 02 77 73 07 63 67
    99 65 04 28 06 16 70 92
    41 41 26 56 83 40 80 70 33
    41 48 72 33 47 32 37 16 94 29
    53 71 44 65 25 43 91 52 97 51 14
    70 11 33 28 77 73 17 78 39 68 17 57
    91 71 52 38 17 14 91 43 58 50 27 29 48
    63 66 04 68 89 53 67 30 73 16 69 87 40 31
    04 62 98 27 23 09 70 98 73 93 38 53 60 04 23
    
    NOTE: As there are only 16384 routes, it is possible to solve this 
    problem by trying every route. However, Problem 67, is the same challenge 
    with a triangle containing one-hundred rows; it cannot be solved by brute 
    force, and requires a clever method! ;o)
    """
    
    #The triangle which will be solved in this problem. 
    triangle = [
        [75],
        [95, 64],
        [17, 47, 82],
        [18, 35, 87, 10],
        [20, 4, 82, 47, 65],
        [19, 1, 23, 75, 3, 34],
        [88, 2, 77, 73, 7, 63, 67],
        [99, 65, 4, 28, 6, 16, 70, 92],
        [41, 41, 26, 56, 83, 40, 80, 70, 33],
        [41, 48, 72, 33, 47, 32, 37, 16, 94, 29],
        [53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14],
        [70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57],
        [91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48],
        [63, 66, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31],
        [4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23]
    ]

    #Traverse all the cells from the second to last row to the apex, 
    #and record the maximum value for each cell by taking the maximum value
    #of either the left or right cell immediately below it -- depending on
    #which is highest. This will eventually give us the maximum value for the
    #apex, which is the answer to this question.
    for i in xrange(len(triangle) - 2, -1, -1):
        for j in xrange(len(triangle[i]) - 1, -1, -1):
            triangle[i][j] += max(triangle[i + 1][j + 1], triangle[i + 1][j])
    
    return triangle[0][0]
    
if __name__ == "__main__":
    cProfile.run("print(get_answer())")
